Eloise, aged six, lived with Nanny in the Plaza Hotel in New York when not in temporary stroppy residence in Paris or Moscow, and ordered from room service such essentials as raisins for Skipperdee, her turtle, and straight Johnny Walker Black for Nanny - "And charge it please, thank you very much". Unseen, very far offstage, was her mother, who knew Coco Chanel, and had size three-and-a-half feet and enough AT&T stock to foot the charge-account bills. Eloise was not adorable but she absolutely did not care, because, besides the full days of a child on conversational terms with all the hotel staff and passing pregnant pigeons, she had a rich fantasy life in which her bawth (pronounced "baaaghth", which we assume she borrowed from the speech of that Edwaarghdian English Nanny in her lisle stockings) was the venue for imaginary events - a motion-picture swimstravaganza or a pirate drama starring "the loosest cannonball in all the Caribbean".

Eloise herself was imagined by Kay Thompson, who had been vocal arranger and coach to the Arthur Freed musicals unit at MGM (she coaxed out Judy Garland's adult persona and Lena Horne's bold tone). She was also a cabaret performer of genius whose numbers swung to jazz syncopation and scat vocals. Scat was the rhythm of life to Eloise in the first four books in which she starred, 1955-1959, but not in the new book, first scheduled for publication in 1964 but abandoned by Thompson, who did not want to be remembered just for Eloise.

Scat, with its wild words and repetitions, shaped both illustrator Hilary Knight's layouts and the movements of Eloise, who, like her creator, was more distinctive of gesture than of face. They were fabulous gestures, those imperious upward and outward flingings of the hands as practised by Eloise, Kay Thompson and, come to think of it, Diana Vreeland, the Vogue fashion empress on whom Thompson based her own performance as Miss Prescott, editor of Quality magazine in the MGM musical Funny Face . Those gestures were about physically projecting the improvisatory voice and the fearless, imperious female personas behind the voice, likely to use a lampshade for a hat, stick out the podgy tum at a fitting with Christian Dior himself, and give the KGB the runaround in cold-war Moscow.

Eloise, as we recall her in her prime (visible in The Ultimate Edition, a compilation of the first four books, plus a biographical insert with tantalising sketches of Thompson in Hollywood), was no spoilt infant, but a miniature Thompson or Vreeland. They believed in women as exotics of independent desire and self-determined action. Eloise might be Colette's vagabond heroine Renée, constructing her solo but not lonely life in yet another hotel room, only, oh hecko, because of that charge account, able to have the kitchen send up clams in season. Behind Eloise, along the corridors of Ritzes and Splendides the length of the Riviera, you can glimpse the tougher women of Edith Wharton: when Eloise dines barefoot outside Aux Deux Magots in Paris, she evidently spent le jour telling Simone de Beauvoir what a drip-drip-drip she was to dote on J-P Sartre.

If true Thompson devotees feel that the long-desired Bawth does not quite achieve the perfection of the originals, it is because of the modification of the voice - Eloise does not riff as she used to, because Manhattan dames don't jive to scat any more - and of those gestures. It doesn't matter that there are entire spreads where Eloise's presence is implied only by her tub's overflow kerplinking on the ballroom floor below - after all, a grande dame knows that when they've been waiting for your re-entrance for 40 years you don't do more but rawther less. What does matter is that the revived Eloise now moves like a brat practised at acting up for snaps: she's looking to the audience, taking applause in mid-twirl. Knight has fudged the era in which Bawth is set: the dial telephones and the movie star surging into a suite are then, while the latest breaking news on Nanny's telly and Eloise's self-aware gestures date it to the present. And that present is definitely diminished, especially if you're only six.